[Paper study] Delay learning and polychronization for reservoir computing

CNNs use spiking neural networks (SNNs) as its backbone. A SNN structure called reservoir and its learning algorithm “reservoir computing” (RC) is described in Paugam-Moisy et al. 2008. She adopted a multi-timescale learning algorithm, which use STDP in millisecond level (synapse level) and a supervised adaptation of axonal transmission delays toward readout neurons coding.

Here is the summary after studying this paper.

This is the network structure,

This is the STDP weight updating rule,

A multiplicative approach is adopted for weight updating where weights are updated as Wij = Wij + α * (Wij – Wmin) * ΔW, if ΔW <=0. And Wij = Wij + α * (Wmax – Wij) * ΔW, if ΔW >=0.

This is the SRM0 spiking neuron model,

This is the pseudo-code for supervised adaptive delays (the multi class version is analogical).

repeatfor each example X=(p, class) of the database{    present the input pattern p;    define the target output neuron according to class;    if (the target output neuron fires less than μms before the non-target one, or fires after it ) then    {        select one triggering connection of the target        output neuron and decrement its delay (-1ms),        except if dmin is reached already;        select one triggering connection of the non-target        output neuron and increment its delay (+1ms),        except if dmax is reached already;    }}until a given maximum learning time is over.

Note that the recognized pattern is represented by the first firing output neuron.

Simulations and visualization of the reservoir will follow in the future posts. Enjoy.